Forces in action

• • A resultant force acting on the object will make the object accelerate in the direction of the net force
  • F = ma
• • The weight of an object on the subject on the Earth is the gravitational force acting on the object
  • An object in free fall has an acceleration, g, of 9.81ms^-2
  • W=mg
• Centre of mass --> An imaginary point where the entire weight of an object appears to act
• Weight --> The gravitational force acting on an object through its centre of mass
• Friction --> The force that arises when two surfaces rub against each other
• Drag --> The resistive force on an object travelling through a fluid (e.g: air and water); the same as friction
• Tension --> The force within a stretched cable or rope
• Upthrust --> An upward buoyancy force acting on an object when it is in a fluid
• Normal contact force --> A force arising when one object rests against another object
• Representing forces:

  In a free body diagram:

  • each force vector is represented by an arrow labelled with the force it represents
  • each arrow is drawn to the same scale ( the longer the arrow, the greater the force)
• On the slope:

  • Weight can be resolved into 2 components, parallel & perpendicular to the slope.
  • Force parallel to the slope =W x sin theta or Fx = mg x sin theta
  • Force perpendicular to the slope = W x cos theta or Fy = mg x cos theta
  • Component of the weight down the slope is responsible for the acceleration of the object down the slope
  • Fy = N = mg x cos theta
• • Drag is a frictional force that opposes the motion of the object
  • Its magnitude depends on several factors, including the speed of the object, the shape of the object, the roughness or textures of the object, and the density of the fluid through which it travels
• • The two most important factors that affect the magnitude of the drag force are speed of the object and its cross-sectional area
  • Drag force is directly proportional to speed^2
• Air resistance --> the drag force experienced by objects moving in air
• During a vertical fall through air or another fluid, the weight of the object remains constant but the drag force increases as the speed increases
• As the object falls

  1. The speed increases & there is an increase in the magnitude of the opposing drag force

  2. The resultant force on the object decreases & the instantaneous acceleration of the object becomes less than g

  3. Eventually the object reaches terminal velocity
• Terminal velocity


  The speed at which an object is falling at a constant rate
• At the instant an object starts to fall, there is no drag force on the object. The total force is equal to the weight
• At terminal velocity, the drag forces on the object is equal and opposite to its weight. At terminal velocity, the object has zero acceleration and its speed is a constant
• The moment of a force:

  • The moment of a force is the turning effect of a force about some axis or point.
  • moment = force x perpendicular distance of the line of action of force from the axis or points of rotation
  • moment = Fx
  • The SI unit for the moment of a force is Nm
• Principle of moments:

  • When a body is in equilibrium, the net force acting on it is zero & its net moment is zero
  • For a body in rotational equilibrium, the sum of the anticlockwise moment about any point is equal to the sum of the clockwise moments about that same point
• Couple --> 2 forces acting parallel and along different lines
• Torque --> the moment of a couple

  • Torque of a couple = one of the forces x perpendicular separation between the forces = Fd
• Forces in equilibrium:

  • To add three vector forces you simply extend the procedure for adding 2 vectors.
  • Arrows are drawn to represent each of the three forces end to end
  • The triangle is closed because the net force is zero & so the object is in equilibrium
• • The resultant of forces F and T must be equal in magnitude to the third force W but in the opposite direction
  • The resultant force vertically must be zero & the resultant horizontal force must also be zero. Therefore the force T can be resolved into its vertical & horizontal components, with T x cos theta = F & T x sin theta = W
• Density:

  • The density of a substance is defined as its mass per unit volume. You can use the following equation to calculate density:
  • Density = mass / volume
• Determining density:

  • The mass can be measured directly using a digital balance
  • For liquids, you can use a measuring cylinder to determine the volume
  • The volume of a regular shaped solid can be calculated from measurements taken with a ruler, digital callipers or a micrometre
  • The volume of irregular solids can be determined by displacement
• Pressure:

  • Pressure is the normal force exerted per unit cross-sectional area. You can use the following equation to calculate pressure, p:
  • pressure = force / area
• Pressure in fluids:

  • Gas & liquids are fluids - substances that can flow
  • Gases, such as air, exert pressure on surfaces because of the constant bombardment by their molecules. Liquids also exert pressure for the same reason.
  • The pressure exerted by the atmosphere of the Earth varies with altitude.
  • At sea level, atmospheric pressure is about 101KPa
• Liquids:

  • density = height x pressure x gravity
  • where h is the height of the liquid column, row is the density of the liquid, and g is the acceleration of free fall ( 9.81 ms^-2)
  • W = mass of column x g
  • W = (density x volume) x g
  • W = density x A x h x g
  • p = density x A x h x g / A = h x density x g
  • density is directly proportional to height, so water pressure increases with depth. The term density shows that denser liquids will exert greater pressure
• Upthrust:

  • force at the top surface = h x density x g x A
  • force at the bottom surface = ( h + x) x density x g x A
  • resultant upwards force = ( h + x) x density x g x A - h x density x g x A = A x x x density x g
• Archimedes' principle --> The upthrust exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.
• • An object will sink if the upthrust is less than the weight of the object.
  • For a floating object, such as ship or a person in water, that upthrust must equal the weight of the object
  • The weight of a floating object must be equal to the weight of the fluid is displaces
• mf = (Wr - Wa) / g
• Floatation:

  • If an object is floating then the forces must be in equilibrium therefore the upthrust must be equal or greater than the weight
  • A floating object will displace its own weight of fluid
  • For an object to float it must have a lower density than the fluid its floating in
  • In equilibrium U=mg
  • Vfd/ Vo = Po/ Pf
• Apparent weight --> the difference between the weight of the object due to gravity and the upthrust from the fluid

  • Apparent weight = real weight - upthrust